Baines, MJ, Hubbard, ME and Jimack, PK orcid.org/0000-0001-9463-7595 (2011) Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations. Communications in Computational Physics, 10 (3). pp. 509-576. ISSN 1815-2406
Abstract
This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | 35R35; 65M60; 76M10; Time-dependent nonlinear diffusion; moving boundaries; finite element method; Lagrangian meshes; conservation of mass |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Dec 2022 14:31 |
Last Modified: | 15 Dec 2022 14:31 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.4208/cicp.201010.040511a |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:166268 |